Pasted

box% sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.2, Release Date: 2020-10-24                     │
│ Using Python 3.8.6. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘
sage: p = 17
sage: f = lambda x: (x^2 + 5) % p
sage: F = lambda S: {f(x) for x in S}
sage: {i for i in range(p)}
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
sage: F(_)
{1, 3, 4, 5, 6, 7, 9, 13, 14}
sage: F(_)
{1, 3, 4, 6, 7, 13, 14}
sage: F(_)
{3, 4, 6, 7, 14}
sage: F(_)
{3, 4, 7, 14}
sage: F(_)
{3, 4, 14}
sage: F(_)
{4, 14}
sage: F(_)
{4, 14}
sage: